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'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] scale structure. [[5/4|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].  
'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] and [[armotonic]] scale structures. [[5/4|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].  
Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy.
Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.
 
{{Cat|Temperaments}}


Extensions of Mabilic include  
Extensions of Mabilic include  


* Trismegistus (best tuned around 527 cents) which finds [[3/2]] at 15 generators up, equating it to three 8/7s ([[Slendric]] temperament) or five 5/4s ([[Magic]] temperament).
* Trismegistus (best tuned around 527 cents) which finds [[3/2]] at 15 generators up, equating it to both three 8/7s ([[Slendric]] temperament) and five 5/4s ([[Magic]] temperament).
** Mnemonic: tris- is Greek for "thrice"; three 8/7's are equated to 3/2; -megistus refers to the Magic mapping of 2.3.5
** Mnemonic: tris- is Greek for "thrice"; three 8/7's are equated to 3/2; -megistus refers to the Magic mapping of 2.3.5
* Semabila (best tuned around 530 cents) which finds [[4/3]] at 10 generators up, equating it to two 8/7s ([[Alpha-dicot|Semaphore]] temperament).
* Semabila (best tuned around 530 cents) which finds [[4/3]] at 10 generators up, equating it to two 8/7s ([[Alpha-dicot|Semaphore]] temperament).
** Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.
*** In fact, Semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.
* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].  
* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].  
In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].
In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].


In any tuning, the sharp generator may be identified wth 28/19. This produces an accurate 2.5.7.19 temperament, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.
In any tuning, the flat fifth generator may be identified wth 28/19. This produces a 2.5.7.19 temperament with a flat tendency for 19, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.


== Intervals ==
== Intervals ==
Trismegistus/Mavila:
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Generators
! rowspan="2" |Tuning
! colspan="4" |Interpretation
|-
|-
! Generators !! Tuning (Trismegistus/Mavila) !! Tuning (Semabila) !! Interpretation (2.5.7) !! Interpretation (Trismegistus) !! Interpretation (Mavila) !! Interpretation (Semabila)
!2.5.7.19
!Trismegistus
!Mavila
!+17.23 interpretation
|-
|-
| -15|| 495|| 450|| || 4/3|| || 21/16
|0
|0
|1/1
|
|
|
|-
|-
| -14|| 1022|| 980|| || || ||  
|1
|527
|19/14
|
|4/3
|23/17, 34/25
|-
|-
| -13|| 349|| 310|| || || || 6/5
|2
|1054
|64/35
|
|16/9, 15/8
|
|-
|-
| -12|| 876|| 840|| || 5/3|| ||  
|3
|381
|'''5/4'''
|
|9/7, 24/19
|
|-
|-
| -11|| 203|| 170|| || || ||  
|4
|908
|'''32/19'''
|
|5/3
|
|-
|-
| -10|| 730|| 700|| || 32/21|| || 3/2
|5
|235
|'''8/7'''
|
|
|
|-
|-
| -9|| 57|| 30|| || || 21/20||  
|6
|762
|25/16
|
|32/21
|
|-
|-
| -8|| 584|| 560|| 7/5|| || ||
|7
|89
|
|21/20
|15/14
|17/16
|-
|-
| -7|| 1111|| 1090|| || 40/21|| 28/15|| 15/8
|8
|616
|10/7
|
|
|23/16
|-
|-
| -6|| 438|| 420|| 32/25|| || 21/16||  
|9
|1143
|
|
|40/21
|
|-
|-
| -5|| 965|| 950|| 7/4|| || || 12/7
|10
|470
|
|21/16
|
|
|-
|-
| -4|| 292|| 280|| || || 6/5||
|11
|997
|
|
|
|34/19
|-
|-
| -3|| 819|| 810|| 8/5|| || 14/9||  
|12
|324
|
|6/5
|
|
|-
|-
| -2|| 146|| 140|| 35/32|| || 16/15, 9/8|| 15/14
|13
|851
|
|
|
|
|-
|-
| -1|| 673|| 670|| || || 3/2||
|14
|178
|
|
|
|17/15
|-
|-
| 0|| 0|| 0|| 1/1|| || ||  
|15
|705
|
|3/2
|
|
|}
Semabila:
{| class="wikitable"
!Generators
!Tuning
!Interpretation (2.3.5.7.19)
!Interpretation (2...29)
|-
|-
| 1|| 527|| 530|| || || 4/3||  
|0
|0
|1/1
|
|-
|-
| 2|| 1054|| 1060|| 64/35|| || 16/9, 15/8|| 28/15
|1
|530
|19/14
|23/17, 34/25, 15/11
|-
|-
| 3|| 381|| 390|| 5/4|| || 9/7||  
|2
|1060
|28/15, 64/35
|
|-
|-
| 4|| 908|| 920|| || || 5/3||  
|3
|390
|5/4, 19/15
|14/11
|-
|-
| 5|| 235|| 250|| 8/7|| || || 7/6
|4
|920
|32/19
|
|-
|-
| 6|| 762|| 780|| 25/16|| || 32/21||
|5
|250
|7/6, 8/7
|15/13
|-
|-
| 7|| 89|| 110|| || 21/20|| 15/14|| 16/15
|6
|780
|25/16, 19/12
|
|-
|-
| 8|| 616|| 640|| 10/7|| || ||
|7
|110
|16/15
|17/16
|-
|-
| 9|| 1143|| 1170|| || || 40/21||
|8
|640
|10/7
|23/16, 16/11
|-
|-
| 10|| 470|| 500|| || 21/16|| || 4/3
|9
|1170
|
|
|-
|-
| 11|| 997|| 1030|| || || ||  
|10
|500
|4/3
|
|-
|-
| 12|| 324|| 360|| || 6/5|| ||
|11
|1030
|
|34/19, 29/16, 20/11
|-
|-
| 13|| 851|| 890|| || || || 5/3
|12
|360
|
|16/13
|-
|-
| 14|| 178|| 220|| || || ||  
|13
|890
|5/3
|
|-
|-
| 15|| 705|| 750|| || 3/2|| || 32/21
|14
|220
|
|17/15
|-
|-
|15
|750
|32/21
|20/13
|}


{{Cat|Temperaments}}
 
{{Navbox regtemp}}
{{Cat|temperaments}}

Latest revision as of 04:30, 9 March 2026

Mabilic is a rank-2 regular temperament based around the antidiatonic and armotonic scale structures. 5/2 is split into three generators which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make 8/7. Mabilic in its basic form is a 2.5.7 subgroup temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.

Extensions of Mabilic include

  • Trismegistus (best tuned around 527 cents) which finds 3/2 at 15 generators up, equating it to both three 8/7s (Slendric temperament) and five 5/4s (Magic temperament).
    • Mnemonic: tris- is Greek for "thrice"; three 8/7's are equated to 3/2; -megistus refers to the Magic mapping of 2.3.5
  • Semabila (best tuned around 530 cents) which finds 4/3 at 10 generators up, equating it to two 8/7s (Semaphore temperament).
    • Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.
      • In fact, Semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.
  • Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to Meantone.

In Meantone, 4 fifths make a 5/4; in Mavila they make a 6/5.

In any tuning, the flat fifth generator may be identified wth 28/19. This produces a 2.5.7.19 temperament with a flat tendency for 19, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.

Intervals

Trismegistus/Mavila:

Generators Tuning Interpretation
2.5.7.19 Trismegistus Mavila +17.23 interpretation
0 0 1/1
1 527 19/14 4/3 23/17, 34/25
2 1054 64/35 16/9, 15/8
3 381 5/4 9/7, 24/19
4 908 32/19 5/3
5 235 8/7
6 762 25/16 32/21
7 89 21/20 15/14 17/16
8 616 10/7 23/16
9 1143 40/21
10 470 21/16
11 997 34/19
12 324 6/5
13 851
14 178 17/15
15 705 3/2

Semabila:

Generators Tuning Interpretation (2.3.5.7.19) Interpretation (2...29)
0 0 1/1
1 530 19/14 23/17, 34/25, 15/11
2 1060 28/15, 64/35
3 390 5/4, 19/15 14/11
4 920 32/19
5 250 7/6, 8/7 15/13
6 780 25/16, 19/12
7 110 16/15 17/16
8 640 10/7 23/16, 16/11
9 1170
10 500 4/3
11 1030 34/19, 29/16, 20/11
12 360 16/13
13 890 5/3
14 220 17/15
15 750 32/21 20/13



View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperament Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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